Agricultural sector is different from economic sector in the way research is conducted.

First of all in English we tend not to label nouns as much as you do in Bahasa Indonesia. An easy example is colours. In English when we mention colours, it isn’t necessary to use the word ‘colour’:

Saya suka warna merah.

I like blue.

Therefore our opening example could easily be written:

Agriculture is different from economics in the way research is conducted.

However, if you must use the word ‘sector’, and if you are talking about specific sectors, then you need to communicate this one exactly:

The agricultural sector is different from the economic sector in the way research is conducted.

If you do not use ‘the’ when you mean this one exactly then you will receive a low score in IELTS for grammar and for coherence and cohesion. If you do not use ‘the’ when you mean this one exactly then your reader will stop reading and think “Does he mean this one exactly, or does he mean one of many, or does he mean all of them everywhere?” You must communicate one of these meanings if you want to be understood clearly.

If you want to communicate one of many then you need to use ‘a’:

Agriculture is a sector that requires different research approaches.(This implies that, in addition to agriculture, there are other sectors, like education, which also require different research approaches.)

If you want to communicate all of them everywhere then you need to use ‘s’:

Government sectors include health, education, agriculture and economics.